The Library
Dimension theory and dynamically defined sets
Tools
Ferguson, Andrew J. (2011) Dimension theory and dynamically defined sets. PhD thesis, University of Warwick.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://webcat.warwick.ac.uk/record=b2677752~S1
Abstract
The first topic of this thesis is concerned with the application of the continuous perturbation
theory of Keller and Liverani to investigate the statistical properties of
dynamical systems with holes. The main result of Chapter 3 is a perturbation result for
a singularly perturbed transfer operator in the setting of subshifts of finite type. Chapter
4 investigates the consequences of this result for an expanding map of a compact metric
space. In this chapter results laws concerning escape rates, extreme value theory, Hausdorff
dimension and return time statistics are derived.
The second main component of the thesis is the study of the orthogonal projection of
dynamically defined sets in the plane. In Chapter 5 we build on the work of Peres and
Shmerkin, proving that if an irrationality condition holds for certain classes of dynamically
defined planar sets then the exceptional set of directions in Marstrand’s theorem
can be computed explicitly.
Item Type: | Thesis (PhD) | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Dimension theory (Algebra), Set theory, Perturbation (Mathematics) | ||||
Official Date: | March 2011 | ||||
Dates: |
|
||||
Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Pollicott, Mark | ||||
Extent: | vi, 126 leaves. | ||||
Language: | eng |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |